Wet human bone for 20-39 year olds has an ultimate compressive strength of ~1.6x

Question

Wet human bone for 20-39 year olds has an ultimate compressive strength of ~1.6x10^4N/cm^2. Consider a person who falls from a height to the ground. Upon landing, the person's kinetic energy is converted to work. If the person decelerates over a distance delta h, we can estimate the average force during the collision by If a person lands stiff-legged on a hard surface and doesn't bounce, the deceleration occurs over a very short distance, deltaa h ~ 1 cm. Since the force is transmitted up the leg, the stress is greatest where the cross-sectional area is least, i.e., the tibia just above the ankle. If A (cross-sectional area of the tibia) ~ 3.4 cm^2, compute how far a 65 kg person can fall and land stiff-legged on both legs without breaking a bone. Assume F is split evenly between two legs. (Hint: F

Explanation / Answer

F = 2 * 1.6 * 10E4 * 3.4 maximum force bones can withstand F = 1.09 * 10E5 N F h    work done in stopping fall m g H      where H is distance person falls F h = m g H H = F h / (m g) = 1.09 * 10E5 * .01 / (65 * 9.8) = 1.71 m

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